Graphing to visualize data

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Graphing to visualize data

• Satish Raghunath
• rsatish_at_alum.rpi.edu
• Shiv Kalyanaraman
• Google Shiv RPI
• shivkuma_at_ecse.rpi.edu
• http//www.ecse.rpi.edu/Homepages/shivkuma

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Overview

• Issues with graphing
• Types of graphs
• Examples of graph usage what you get out of
  them
• Art how to choose what graph to use?
• Graphing Tools
• Pitfalls and mistakes in graphing
• Advanced visualization
• In class work reviewing graphing use in selected
  technical papers

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Thoughts on Presentation Styles

• Primary purpose illustrate to help understand

The goal of simulation is intuition, not
numbers," - R.W. Hamming

• Corollary dont dump data on the reader.
• Distill it into presentations that give insight
  instead

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Descriptive Statistics

• Involves
• Collecting Data
• Presenting Data
• Characterizing Data
• Understanding data distill insights!

50
25
0
Q1
Q2
Q3
Q4
?X 30.5 S2 113
Insights Somewhat skewed Bell shape perhaps a
Poisson (distrn) would fit?
Statistics obtained from data
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To graph or not to graph

• Use graphs when
• Trends in data are not obvious
• It is hard to explain the X-Y relationship in
  words
• Consider tables if
• The number of data-points are small
• Reader might find exact value of data-points
  useful

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Summary Table Frequencies

• 1. Lists Categories No. Elements in Category
• 2. Obtained by Tallying Responses in Category
• 3. May Show Frequencies (Counts), or Both

Row Is Category
Tally
Major
Count
Accounting
130
Economics
20
Management
50
Total
200
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Example Tables from Networking
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What kind of graph?

• Pie-charts to depict fraction of a whole
• Bar-charts when data-points few and table is not
  suitable
• Line-plots when there are a lot of data-points
• Box-plots if statistical inference is drawn
  shows 1st, 2nd, 3rd quartile for each point.
• Scatter-plots, 3-d plots only if necessary
  AVOID complex graphs

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Pie Chart

• 1. Shows Breakdown of Quantity into Categories
• 2. Useful for Showing Relative Differences
• 3. Angle Size
• (360) x (Percent)

Majors
Mgmt.
Econ.
25
10
36
Acct.
65
(360) (10) 36
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Pie Chart Networking Example
Source http//www.caida.org/bhuffake/papers/skit
viz/
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Another eg VPN Classification
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Bar Chart
Horizontal Bars for Categorical Variables
Bar Length Shows Frequency or
Major
Mgmt.
Equal Bar Widths
Econ.
1/2 to 1 Bar Width
Acct.
0
50
100
150
Zero Point
Frequency
Percent Used Also
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Networking Example Bar Chart
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Example Analysis with Bar Charts

• LT-TCP is able to
• reduce timeouts drastically
• keep the queue non-empty maximizing throughput
  and capacity utilization.
• minimize use of FEC to level needed

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Histogram for distributions
Class
Freq.
Count
15 but lt 25
3
5
25 but lt 35
5
35 but lt 45
2
4
Frequency Relative Frequency Percent
3
Bars Touch
2
1
0
0 15 25 35 45 55
Lower Boundary
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Recall Real Example Histogram

• What is the fairness between TCP goodputs when we
  use different queuing policies?
• What is the confidence interval around your
  estimates of mean file size?
• Note distribution need not just be a
  probability/frequency distribution

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Dot Chart or Scatterplots
Major
Line Length Shows Frequency or
Like Horizontal Bar Chart
Mgmt.
Horizontal Lines for Categorical Variables
Equal Spacing
Econ.
Acct.
0
50
100
150
Zero Point
Frequency
Percent Used Also
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Scatter Plots
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Scatter plots with trends
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WiFi Analysis Scatter Plots

• http//www.sigcomm.org/sigcomm2004/papers/p442-agu
  ayo1111.pdf

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Line ChartsExampleComparative Performance
Note also plots confidence intervals!
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Line Plots for Distributions Example

• Hop count and RTT distributions

Source http//www.caida.org/bhuffake/papers/skit
viz/
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Recall Distribution Shape

• 1. Describes How Data Are Distributed
• 2. Measures of Shape
• Skew Symmetry

Right-Skewed
Left-Skewed
Symmetric
Mean

Median

Mode
Mean


Median


Mode
Mode

Median

Mean
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Box Plot

• Graphical Display of Data Using5-Number Summary

Median
Q
Q
X
X
3
1
largest
smallest
4
6
8
10
12
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3D Graphs Example

• Illustrates a complex parameter response surface
  ...

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3D Plots N/w Example Code Red Worm Analysis

• http//www.prism.uvsq.fr/users/qst/Tomography/Arti
  cles_jmf/renesys_bgp_instabilities2001.pdf
• http//www.caida.org/outreach/isma/0112/talks/andy
  o/index.pdf
• http//www.renesys.com/resource_library/Renesys-NA
  NOG23.pdf

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Contd
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Tools Gnuplot

• To use with data-generating programs for
  repetitive plotting
• E.g. generate the plot of throughput for every 1
  hour interval in the last week.
• http//www.gnuplot.info
• TIP Export gnuplot plots as .fig file and edit
  it in xfig for greater flexibility

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Tools XmGrace

• For more intricate details (e.g., creating
  error-bars, different shades for bar-charts)
  GUI-driven, very user friendly.
• http//plasma-gate.weizmann.ac.il/Grace/
• Exports images to EPS (good for LaTeX documents),
  PNG (good for PowerPoint) etc.
• Can also run on Windows on top of Cygwin!

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Tools MATLAB

• For complex 3-d and other statistical plots like
  box-plots, scatter-plots and in general if
  enormous quantities of data is involved.
• http//www.mathworks.com

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Tools Excel Data Presentations

• Open up Excel to a new Worksheet.
• Code a data set as below
• Blue 34
• White 68
• Red 25
• Green 50
• Explore simple data presentation possibilities

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Graphs things to watch out

• Purpose illustrate entire time-series or
  response distribution
• Label the x- and y-axis
• Check what units the x- and y-axes are in (not
  goats or sheep!)
• Check if either scale is logarithmic (changes
  meaning)
• Check where is the origin (or zero point) for
  each axis!
• After understanding WHAT is being plotted, close
  your eyes and ask
• what will different patterns on this graph imply
  (relative to what I want to understand)?
• See if the relative performance is over- or
  under-emphasized (if two systems are being
  compared)
• Several examples in the Jain textbook

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Errors in Presenting Data

• 1. Using Chart Junk
• 2. No Relative Basis in Comparing Data Batches
• 3. Compressing the Vertical Axis
• 4. No Zero Point on the Vertical Axis

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Chart Junk
Bad Presentation
Good Presentation
Minimum Wage
Minimum Wage

1960 1.00
4
1970 1.60
2
1980 3.10
0
1990 3.80
1960
1970
1980
1990
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No Relative Basis
Good Presentation
Bad Presentation
As by Class
As by Class
Freq.

300
30
200
20
100
10
0
0
FR
SO
JR
SR
FR
SO
JR
SR
36
Compressing Vertical Axis
Good Presentation
Bad Presentation
Quarterly Sales
Quarterly Sales


50
200
25
100
0
0
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
37
No Zero Point on Vertical Axis
Good Presentation
Bad Presentation
Monthly Sales
Monthly Sales


45
60
42
40
39
20
0
36
J
M
M
J
S
N
J
M
M
J
S
N
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Graphing Practices In pictures ?
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Graphing Practices
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Graphing Practices
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Graphing Practices.
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Checklist In textbook
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More Complex Visualizations

• Internet topology aspects
• CAIDA skitter project

http//www.caida.org/tools/measurement/skitter/vis
ualizations.xml
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More
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The End